TY - BOOK AU - AU - ED - SpringerLink (Online service) TI - An Introduction to Nonlinear Functional Analysis and Elliptic Problems T2 - Progress in Nonlinear Differential Equations and Their Applications SN - 9780817681142 AV - QA319-329.9 U1 - 515.7 23 PY - 2011/// CY - Boston PB - Birkhuser Boston KW - Mathematics KW - Differentiable dynamical systems KW - Functional analysis KW - Differential equations, partial KW - Functional Analysis KW - Partial Differential Equations KW - Dynamical Systems and Ergodic Theory N1 - Notation -- Preliminaries -- Some Fixed Point Theorems -- Local and Global Inversion Theorems -- Leray-Schauder Topological Degree -- An Outline of Critical Points -- Bifurcation Theory -- Elliptic Problems and Functional Analysis -- Problems with A Priori Bounds -- Asymptotically Linear Problems -- Asymmetric Nonlinearities -- Superlinear Problems -- Quasilinear Problems -- Stationary States of Evolution Equations -- Appendix A Sobolev Spaces -- Exercises -- Index -- Bibliography; ZDB-2-SMA N2 - This self-contained textbook provides the basic, abstracttoolsused innonlinear analysisand their applications to semilinear elliptic boundary value problems.By firstoutlining the advantages and disadvantages of each method, this comprehensive textdisplays how variousapproachescan easily beappliedto a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problemsis divided into two parts: the first discusses keyresults such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, LeraySchauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems. The exposition is driven by numerous prototype problems and exposes a variety of approaches tosolving them. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is apractical text for an introductory course or seminar on nonlinear functional analysis UR - http://dx.doi.org/10.1007/978-0-8176-8114-2 ER -